Problem: Express your answer as a mixed number simplified to lowest terms. $15\dfrac{2}{20}-9\dfrac{2}{12} = {?}$
Solution: Simplify each fraction. $= {15\dfrac{1}{10}} - {9\dfrac{1}{6}}$ Find a common denominator for the fractions: $= {15\dfrac{3}{30}}-{9\dfrac{5}{30}}$ Convert ${15\dfrac{3}{30}}$ to ${14 + \dfrac{30}{30} + \dfrac{3}{30}}$ So the problem becomes: ${14\dfrac{33}{30}}-{9\dfrac{5}{30}}$ Separate the whole numbers from the fractional parts: $= {14} + {\dfrac{33}{30}} - {9} - {\dfrac{5}{30}}$ Bring the whole numbers together and the fractions together: $= {14} - {9} + {\dfrac{33}{30}} - {\dfrac{5}{30}}$ Subtract the whole numbers: $=5 + {\dfrac{33}{30}} - {\dfrac{5}{30}}$ Subtract the fractions: $= 5+\dfrac{28}{30}$ Combine the whole and fractional parts into a mixed number: $= 5\dfrac{28}{30}$ Simplify to lowest terms: $= 5\dfrac{14}{15}$